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uh let's get on to our next talk

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and the next talk

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is going to be by uh professor paul

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thibodeau

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uh

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paul is a professor at the university of

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arkansas

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he got his bachelor's in science in

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physics and mathematics at san diego

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state

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and his phd at the university of

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pennsylvania

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he works on surface physics and

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using scanning tunneling microscope

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microscopy

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and in particular for the last 10 years

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or so he's been looking at freestanding

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graphene films

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if you are like me you've been aware of

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paul's recent work for the last few

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years and have really been scratching

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your head about it because he has some

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intriguing and fascinating results in

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terms of harvesting essentially

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brownian type motion in graphene

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and uh

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it's yeah

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it's very interesting and

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may really require some some basic

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rethinks of

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a lot of the uh

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thermal vibration concepts that we've

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had so paul

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please uh the

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talk title is charging capacitors using

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graphene fluctuations

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paul

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great yeah thank you for that you know

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um

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i guess my video has been stopped by

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somebody so you can't really see me but

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paul you can just start the your video

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yourself

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you know it won't let me i won't let you

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huh it says you cannot start your video

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because the host has stopped it but

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that's okay can you see my screen

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uh yes

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okay

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so my video's off but it's not um not my

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doing here sorry

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um

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all right

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great your the host has asked me so

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let's let's start it okay all right

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great thank you

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okay well thank you for that

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introduction garrett also um yeah well

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i'm paul thibodeau of the university so

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let me just get that out of the way and

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um

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garrett and charles

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for

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you know talking to me and being

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interested in my research um it's i've

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had great conversations with them i'd

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also like to say that the talk that

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daniel gave was excellent that's the

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first i've heard his talks

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it was really well done

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i do want to clarify a little bit that

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my research is not about

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searching for violations the second law

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my research is about harvesting energy

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from the environment so i'm just going

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to kind of focus on that part of it but

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i do talk about the laws of physics of

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course

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and so let me just get started with that

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start a little timer here too my talk

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will probably take 35 minutes so it'll

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be plenty of time for questions if there

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are any

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i'm going to talk about charging

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capacitors using graphene fluctuations

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this is the circuit

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that i'm going to use

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we've actually been studying this

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circuit for about five years now

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i'm going to show you that this circuit

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can steal energy from the thermal

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surroundings

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these results actually were really just

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discovered and presented here first it

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was kind of good timing that i got

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contacted by

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daniel charles and garrett

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in the first part i'm going to talk

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about the deterministic

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[Music]

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properties or solutions if you like of

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this circuit

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and then the second part i'll talk about

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the stitch stochastic part

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see if this is alright

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okay

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so in the deterministic part

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it's this thing up here

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let me get

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um

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so the deterministic part all right

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graphene it's only one atom thick

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therefore it's extremely flexible a

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measure of that flexibility is called

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the flexural rigidity it's given by d

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here's the formula for it the important

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part is it has this parameter h to the

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third power

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where h is the thickness of the plate

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so graphene membrane is only about one

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nanometer thick

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whereas

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you could probably make a silicon

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nitride cantilever at best 10 nanometers

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that'd be the thinnest

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so right here

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that would tell you that the graphene is

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going to be a thousand times more

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flexible than this cantilever

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what that translates into if you think

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it kind of like hooks law or whatever if

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if a one nano newton force moves the

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silicon nitride cantilever a certain

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distance

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then a piconewton force

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a thousand times smaller could move the

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graphene the same distance

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so it's very flexible and easy to move

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when graphene moves how does that result

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i like to turn people to this paper

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inside of the physics teacher

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it basically talks about variable

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capacitors

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if you look at the definition the

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capacitance is how much charge it can

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store

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divided by the voltage you've applied to

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it

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change in charge

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here's a nice illustration of a parallel

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plate capacitor connected to a battery

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and it has four units of charge on it if

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we applied a force to this plate and

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pulled it to the right

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the capacitance would go down so the

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charge has to go down

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so what will happen is let's say these

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two charges will flow

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counterclockwise

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they'll go backwards through the battery

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and recharge it if it's rechargeable

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battery and then come around here to

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cancel these charges and the force that

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pulled that plate apart that's what's

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doing the work here

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so that's basically the fundamental

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operation of our

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uh circuit as well so as the distance

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between the graphene and the electrode

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changes because the graphene's so

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flexible it's moving all the time under

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the slightest influence

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the capacitance will increase and

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decrease and then the charge on the

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graphene will also increase and decrease

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when current flows in this circuit

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clockwise

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it'll go through diode 1 and charge

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capacitor c1 to complete the circuit

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when it flows counterclockwise

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it'll charge c2 going through d2 and go

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back to complete the circuit so that's

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basically how the energy harvesting work

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take an ac signal and charge these two

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we had an illustration we made of this a

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while back see if i can get it to go

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here we go

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um this is the idea so basically there's

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the graphing fluctuating nice slow

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motion

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as the capacitance increases the charge

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increase there it took power from the

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battery but now the

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battery got recharged and we also made

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it go through that storage capacity this

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is like that c2 over here

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and as the graphene keeps moving it'll

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keep forcing charge onto the capacitor

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and off the capacitor

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we use these diodes to

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redirect the current

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so it can charge charge up the storage

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passion then we can use that

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all right what about the efficiency

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so we actually built this circuit uh

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here's a variable on a macroscopic scale

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so here is a

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variable capacitor you can vary the

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capacitance by turning this rod here

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here all these plates are overlapping

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one another to give the maximum

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capacitance in this picture they're

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not overlapping at all and it gives you

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the minimum capacitance

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this plot here shows the capacitance as

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a function of rotation it starts off at

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about one nanofarad drops to point one

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moves in a nice linear line actually and

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goes back to one again as you continue

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to rotate it through a full rotation

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this is a really high grade military

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variable capacitor

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that we did with this experience that

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has this nice precise capability we

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hooked it up to this circuit that's the

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same circuit we used transistors wired

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as diodes here they were a little bit

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better for this application

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and so

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what happens is that when the current

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goes clockwise it'll charge capacitor

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one

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and when the current goes

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counterclockwise it goes backwards

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through the battery

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and charges capacitor 2.

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here we're showing the voltage on

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capacitor 2 as a function of the number

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rotation so you can see that it's

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charging it up

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we can also measure the current flowing

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into capacitor 2 in time it has kind of

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a spiky nature it's pretty small it's

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only 10 nano amps

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um but it's wider here as the time goes

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on or the rotation's gone it gets

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narrower so the current is dropping as

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the capacitor is charging up

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the interesting thing that we found was

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the circuit has fifty percent efficiency

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when operated at the maximum power point

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so even though the current was small

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here

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and people thought okay well it'll work

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but the efficiency will be terrible

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turns actually the efficiency is

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excellent fifty 50 efficiency is very

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good

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here's a little video of it running

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so here's the variable capacitor being

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turned by a motor so it's nice and

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smooth and continuous

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this volt meter back here is measuring

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the voltage on capacitor 2 you can see

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it's increasing in the negative

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direction and here's a little breadboard

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and in fact we've been pushing this

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forward

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as hard as we can and we've actually

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made

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a first integrated circuit or a chip

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in 2021

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this is a five millimeter by five

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millimeter chip we had it made at taiwan

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semiconductor

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inside the chip are this is the diode

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circuitry

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and it connects to these bonding pads

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around the outside so there's a bunch of

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bonding pads here

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there's a big section here in the middle

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which is um basically we left blank

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and when the chips came back we did post

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processing we built an array of these

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graphene

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electrode

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systems on this chip

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and then connected those

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uh things to the bonding pads or the

290
00:10:49,430 --> 00:10:47,519
circuitry below

291
00:10:51,030 --> 00:10:49,440
you can see the graphene here this is

292
00:10:52,310 --> 00:10:51,040
graphene is covering the whole upper

293
00:10:54,150 --> 00:10:52,320
half of the chip

294
00:10:55,110 --> 00:10:54,160
touching the bonding pads naturally

295
00:10:56,870 --> 00:10:55,120
there

296
00:11:00,870 --> 00:10:56,880
the lower edge of the graphene can see

297
00:11:04,230 --> 00:11:00,880
right here so we're pushing this forward

298
00:11:08,470 --> 00:11:06,230
all right so so that's what i'm going to

299
00:11:10,230 --> 00:11:08,480
call the deterministic part

300
00:11:12,389 --> 00:11:10,240
let me ask this question so when the

301
00:11:14,389 --> 00:11:12,399
graphene shakes some really questionable

302
00:11:16,470 --> 00:11:14,399
points i'll get to the question below so

303
00:11:17,990 --> 00:11:16,480
when graphene shakes

304
00:11:20,389 --> 00:11:18,000
current flows

305
00:11:22,870 --> 00:11:20,399
and the diodes charge c1 c2 so hopefully

306
00:11:24,470 --> 00:11:22,880
i convinced you of that

307
00:11:26,870 --> 00:11:24,480
but here's the question

308
00:11:29,910 --> 00:11:26,880
will c1 and c2 will the capacitors

309
00:11:31,910 --> 00:11:29,920
charge if the only force acting

310
00:11:33,190 --> 00:11:31,920
is the thermal force

311
00:11:37,110 --> 00:11:33,200
and it's everything's at the same

312
00:11:41,030 --> 00:11:39,190
well what's motivating this we had some

313
00:11:42,870 --> 00:11:41,040
early success

314
00:11:44,550 --> 00:11:42,880
we were able to show that the brownian

315
00:11:47,910 --> 00:11:44,560
motion that's that thermal motion of

316
00:11:50,150 --> 00:11:47,920
graphene could power a circuit

317
00:11:52,389 --> 00:11:50,160
we did this using our scanning tunneling

318
00:11:54,069 --> 00:11:52,399
microscope chamber this is a tem grid

319
00:11:55,750 --> 00:11:54,079
with graphene overlay you can see the

320
00:11:57,590 --> 00:11:55,760
graphene film here

321
00:11:59,829 --> 00:11:57,600
this is pretty much the same circuit

322
00:12:03,030 --> 00:11:59,839
except we have ammeters here measuring

323
00:12:05,670 --> 00:12:03,040
the current in these two channels

324
00:12:07,110 --> 00:12:05,680
and so we could do that we did power a

325
00:12:09,110 --> 00:12:07,120
circuit

326
00:12:12,470 --> 00:12:09,120
and we determined that the power density

327
00:12:14,389 --> 00:12:12,480
was one pico watt per micron squared

328
00:12:16,790 --> 00:12:14,399
if you convert the units on that that's

329
00:12:19,190 --> 00:12:16,800
one watt per meter squared

330
00:12:22,069 --> 00:12:19,200
there was a really nice study done in

331
00:12:24,389 --> 00:12:22,079
2018 on draw your attention to

332
00:12:26,629 --> 00:12:24,399
that studied wind farms all around the

333
00:12:29,430 --> 00:12:26,639
world there's thousands of them and they

334
00:12:31,910 --> 00:12:29,440
found out the wind farms produce 0.5

335
00:12:33,750 --> 00:12:31,920
watts per meter squared so actually

336
00:12:35,829 --> 00:12:33,760
we're on the par with

337
00:12:38,389 --> 00:12:35,839
wind power here

338
00:12:40,150 --> 00:12:38,399
solar farms all over the world

339
00:12:42,629 --> 00:12:40,160
were also studied they only produce

340
00:12:44,069 --> 00:12:42,639
about five watts per meter squared

341
00:12:45,990 --> 00:12:44,079
so it's a

342
00:12:47,750 --> 00:12:46,000
viable it's worth pursuing i guess is

343
00:12:49,110 --> 00:12:47,760
what we would say

344
00:12:51,670 --> 00:12:49,120
this paper

345
00:12:53,750 --> 00:12:51,680
obtained a lot of attention

346
00:12:55,990 --> 00:12:53,760
one way you can see measure that is

347
00:12:59,110 --> 00:12:56,000
through this old metric score if it got

348
00:13:01,269 --> 00:12:59,120
a 286 well it's up to 286

349
00:13:01,990 --> 00:13:01,279
most of my papers get a zero or a one in

350
00:13:03,910 --> 00:13:02,000
this

351
00:13:05,829 --> 00:13:03,920
metric score

352
00:13:07,829 --> 00:13:05,839
honestly they get a higher alt metric

353
00:13:10,629 --> 00:13:07,839
score there were other papers in that

354
00:13:12,150 --> 00:13:10,639
year if you found a vaccine for covid

355
00:13:14,550 --> 00:13:12,160
and published that you got a higher

356
00:13:17,110 --> 00:13:14,560
altmetric score or if you found water on

357
00:13:18,629 --> 00:13:17,120
the moon so this is a big score

358
00:13:20,870 --> 00:13:18,639
and actually i got

359
00:13:22,949 --> 00:13:20,880
close to a thousand emails

360
00:13:23,750 --> 00:13:22,959
i'd say most were fan mail but there's a

361
00:13:25,110 --> 00:13:23,760
few

362
00:13:25,990 --> 00:13:25,120
haters out there

363
00:13:27,269 --> 00:13:26,000
um

364
00:13:28,949 --> 00:13:27,279
usually the questions were about the

365
00:13:32,629 --> 00:13:28,959
second law so i think that's partly why

366
00:13:36,150 --> 00:13:33,750
all right

367
00:13:38,150 --> 00:13:36,160
so let's move to part two the stochastic

368
00:13:40,069 --> 00:13:38,160
part so to do that we're going to talk

369
00:13:41,670 --> 00:13:40,079
about brownian motion and the ido

370
00:13:43,910 --> 00:13:41,680
launchment equation

371
00:13:46,470 --> 00:13:43,920
this is basically newton's second law

372
00:13:48,389 --> 00:13:46,480
but with a stochastic driving force so

373
00:13:50,629 --> 00:13:48,399
i've written that here

374
00:13:52,150 --> 00:13:50,639
this is m a

375
00:13:54,710 --> 00:13:52,160
the forces that are acting there's a

376
00:13:56,790 --> 00:13:54,720
drag force that's involved in brownian

377
00:13:59,350 --> 00:13:56,800
motion that basically is trying to bring

378
00:14:01,430 --> 00:13:59,360
the brownian particle to a dead stop and

379
00:14:03,590 --> 00:14:01,440
it will bring it to a dead stop

380
00:14:07,350 --> 00:14:03,600
but then there's a thermal force

381
00:14:09,430 --> 00:14:07,360
that is also present and this thing

382
00:14:11,189 --> 00:14:09,440
transfers energy from the thermal

383
00:14:12,949 --> 00:14:11,199
environment to the brownian particle

384
00:14:14,389 --> 00:14:12,959
gives its energy to the particle and

385
00:14:16,790 --> 00:14:14,399
gets moving again let me show this

386
00:14:19,110 --> 00:14:16,800
little video so this is like our

387
00:14:21,829 --> 00:14:19,120
brownian particle this is in 3d but our

388
00:14:24,069 --> 00:14:21,839
our solutions will be in one dimension

389
00:14:25,910 --> 00:14:24,079
the drag force is taking the kinetic

390
00:14:27,269 --> 00:14:25,920
energy of the particle and giving it to

391
00:14:29,590 --> 00:14:27,279
the environment

392
00:14:31,189 --> 00:14:29,600
and then this force over here is taking

393
00:14:34,230 --> 00:14:31,199
the energy from the environment and

394
00:14:35,990 --> 00:14:34,240
giving it back to the particle

395
00:14:37,670 --> 00:14:36,000
this thermal force looks a lot like this

396
00:14:39,910 --> 00:14:37,680
it's basically kind of a noisy

397
00:14:41,990 --> 00:14:39,920
stochastic signal

398
00:14:45,750 --> 00:14:42,000
what we want to do is steal energy from

399
00:14:49,509 --> 00:14:48,069
notice the thermal force is zero if t

400
00:14:50,870 --> 00:14:49,519
equals zero the temperature is zero

401
00:14:52,470 --> 00:14:50,880
that's how we know it's the thermal

402
00:14:55,269 --> 00:14:52,480
force

403
00:14:57,590 --> 00:14:55,279
also notice that eta this parameter

404
00:14:59,750 --> 00:14:57,600
is in both places it's both here in the

405
00:15:01,750 --> 00:14:59,760
thermal force and in the drag force this

406
00:15:03,829 --> 00:15:01,760
ensures that we reach thermodynamic

407
00:15:07,189 --> 00:15:03,839
equilibrium this was a big breakthrough

408
00:15:09,670 --> 00:15:07,199
in the fluctuation dissipation theorem

409
00:15:12,310 --> 00:15:09,680
basically what it says is

410
00:15:13,750 --> 00:15:12,320
if the particle is giving energy to the

411
00:15:15,670 --> 00:15:13,760
environment

412
00:15:17,670 --> 00:15:15,680
and the energy is giving and sorry in

413
00:15:19,910 --> 00:15:17,680
the environment is giving energy to the

414
00:15:21,990 --> 00:15:19,920
particle if those two

415
00:15:24,310 --> 00:15:22,000
processes are equal to each other then

416
00:15:26,629 --> 00:15:24,320
we'll reach thermodynamic equilibrium

417
00:15:28,470 --> 00:15:26,639
and that's basically saying that the

418
00:15:30,389 --> 00:15:28,480
kinetic energy

419
00:15:33,269 --> 00:15:30,399
one-half mv squared is equal to the

420
00:15:37,670 --> 00:15:33,279
thermal energy one-half kbt so we by

421
00:15:40,389 --> 00:15:38,790
graphene

422
00:15:42,870 --> 00:15:40,399
has a ripley structure this is an

423
00:15:44,870 --> 00:15:42,880
important property we think of graphing

424
00:15:46,550 --> 00:15:44,880
the surface of graphene like this except

425
00:15:48,790 --> 00:15:46,560
dynamic more like the surface of the

426
00:15:50,310 --> 00:15:48,800
ocean it has waves on it it has

427
00:15:52,550 --> 00:15:50,320
curvature

428
00:15:55,269 --> 00:15:52,560
we call these ripples the ripples can

429
00:15:57,110 --> 00:15:55,279
have a convex curvature or a concave

430
00:15:58,870 --> 00:15:57,120
curvature and they can invert their

431
00:16:02,069 --> 00:15:58,880
curvature as well so here's kind of an

432
00:16:03,590 --> 00:16:02,079
illustration of a ripple that is convex

433
00:16:04,949 --> 00:16:03,600
and it could flip over and become

434
00:16:07,509 --> 00:16:04,959
concave

435
00:16:09,189 --> 00:16:07,519
we've done molecular dynamic simulations

436
00:16:11,670 --> 00:16:09,199
of graphing ripples and sure enough they

437
00:16:14,069 --> 00:16:11,680
do do that so here's a ripple

438
00:16:17,829 --> 00:16:14,079
having this random motion but

439
00:16:18,710 --> 00:16:17,839
at a positive value here and then

440
00:16:21,110 --> 00:16:18,720
at

441
00:16:23,110 --> 00:16:21,120
this point in time it

442
00:16:25,910 --> 00:16:23,120
flips its curvature from convex to

443
00:16:27,590 --> 00:16:25,920
concave and goes on a long excursion and

444
00:16:28,949 --> 00:16:27,600
now sits down here for a while and goes

445
00:16:30,550 --> 00:16:28,959
back again

446
00:16:32,550 --> 00:16:30,560
so that means it lives in what we call a

447
00:16:34,470 --> 00:16:32,560
double well potential can either be at

448
00:16:36,949 --> 00:16:34,480
this point five or minus point five

449
00:16:39,269 --> 00:16:36,959
instead of zero so the force from the

450
00:16:41,509 --> 00:16:39,279
ripple double well potential that needs

451
00:16:43,430 --> 00:16:41,519
to be added in so we add that in

452
00:16:46,150 --> 00:16:43,440
it what it what we found it does is it

453
00:16:48,230 --> 00:16:46,160
lowers the frequency of the

454
00:16:50,230 --> 00:16:48,240
energy which is helpful for energy

455
00:16:53,350 --> 00:16:50,240
harvesting we still have this there's

456
00:16:54,470 --> 00:16:53,360
still thermodynamic equilibrium

457
00:16:56,310 --> 00:16:54,480
all right

458
00:16:58,790 --> 00:16:56,320
we're going to hook it up to a circuit

459
00:17:02,870 --> 00:16:58,800
it turns out electrons in a circuit also

460
00:17:04,710 --> 00:17:02,880
have are basically have brownian motion

461
00:17:06,949 --> 00:17:04,720
so there's an edo launchment equation

462
00:17:08,870 --> 00:17:06,959
for this as well let's start over here

463
00:17:10,230 --> 00:17:08,880
here's a circuit with a capacitor and a

464
00:17:12,150 --> 00:17:10,240
resistor i'll tell you this can't

465
00:17:14,470 --> 00:17:12,160
harvest energy

466
00:17:16,390 --> 00:17:14,480
i'll show that it can't

467
00:17:18,390 --> 00:17:16,400
what we start off with is kirchhoff's

468
00:17:21,429 --> 00:17:18,400
loop law it says that the voltage on

469
00:17:23,029 --> 00:17:21,439
this capacitor is q over c but it's also

470
00:17:24,630 --> 00:17:23,039
i times r

471
00:17:26,069 --> 00:17:24,640
instead of using the resistance we're

472
00:17:28,710 --> 00:17:26,079
going to use the conductance it's just

473
00:17:30,870 --> 00:17:28,720
one over the resistance so i equals the

474
00:17:34,390 --> 00:17:30,880
conductance times the voltage

475
00:17:36,630 --> 00:17:34,400
we put that here so i is dq dt

476
00:17:39,270 --> 00:17:36,640
it's the conductance times the voltage

477
00:17:41,669 --> 00:17:39,280
and then we add the thermal current this

478
00:17:43,990 --> 00:17:41,679
time so here the resistance is trying to

479
00:17:45,029 --> 00:17:44,000
bring the electron to a dead stop and it

480
00:17:46,789 --> 00:17:45,039
will

481
00:17:48,870 --> 00:17:46,799
then the thermal

482
00:17:51,909 --> 00:17:48,880
current comes in gives it a kick and

483
00:17:53,750 --> 00:17:51,919
starts it moving again

484
00:17:56,310 --> 00:17:53,760
the thermal current is zero if the

485
00:17:58,310 --> 00:17:56,320
temperature is zero

486
00:18:00,390 --> 00:17:58,320
notice mu is in both places again so

487
00:18:02,710 --> 00:18:00,400
this is going to ensure that we satisfy

488
00:18:05,510 --> 00:18:02,720
the fluctuation dissipation theorem and

489
00:18:07,190 --> 00:18:05,520
that we're in thermodynamic equilibrium

490
00:18:08,789 --> 00:18:07,200
what that tells us here though is that

491
00:18:15,110 --> 00:18:08,799
the

492
00:18:17,669 --> 00:18:15,120
one half c

493
00:18:19,590 --> 00:18:17,679
voltage squared u squared if we

494
00:18:21,590 --> 00:18:19,600
rearrange that it says u squared the

495
00:18:24,150 --> 00:18:21,600
variance of u we say

496
00:18:26,630 --> 00:18:24,160
is kbt divided by c so notice the

497
00:18:27,750 --> 00:18:26,640
smaller c is the larger the voltage

498
00:18:29,510 --> 00:18:27,760
becomes

499
00:18:31,909 --> 00:18:29,520
so i plotted that here so even though

500
00:18:33,909 --> 00:18:31,919
the even though the mean voltage or the

501
00:18:36,310 --> 00:18:33,919
average voltage is zero

502
00:18:38,630 --> 00:18:36,320
the fluctuations

503
00:18:40,870 --> 00:18:38,640
or the standard deviation of the voltage

504
00:18:41,990 --> 00:18:40,880
increases dramatically as c becomes

505
00:18:46,150 --> 00:18:42,000
smaller and we're going to take

506
00:18:49,590 --> 00:18:47,669
all right let's replace the wrist

507
00:18:50,950 --> 00:18:49,600
resistor with a diode that we can't do

508
00:18:52,230 --> 00:18:50,960
anything with the resistor we need a

509
00:18:56,070 --> 00:18:52,240
diode

510
00:19:00,070 --> 00:18:56,080
tell you this circuit will not harvest

511
00:19:02,549 --> 00:19:00,080
energy either i can prove that i will

512
00:19:05,270 --> 00:19:02,559
the diode is special in the sense it has

513
00:19:07,350 --> 00:19:05,280
a non-linear conductance so it has a mu

514
00:19:09,270 --> 00:19:07,360
prime basically the ra there's a rate of

515
00:19:10,549 --> 00:19:09,280
change in the diode conductance with

516
00:19:11,750 --> 00:19:10,559
voltage

517
00:19:14,470 --> 00:19:11,760
that's

518
00:19:16,230 --> 00:19:14,480
an added effect with a resistor this

519
00:19:17,669 --> 00:19:16,240
would be equal to zero but in a diode

520
00:19:20,070 --> 00:19:17,679
it's not zero

521
00:19:22,470 --> 00:19:20,080
well look what happens to the ito

522
00:19:24,789 --> 00:19:22,480
longevin equation we get this extra term

523
00:19:26,390 --> 00:19:24,799
stuck in here this is called the thermal

524
00:19:29,830 --> 00:19:26,400
drift current

525
00:19:32,230 --> 00:19:29,840
zero see that

526
00:19:34,549 --> 00:19:32,240
it's also zero if mu prime goes to zero

527
00:19:37,590 --> 00:19:34,559
so if we were if this diode turns into a

528
00:19:39,590 --> 00:19:37,600
resistor it's gone

529
00:19:41,110 --> 00:19:39,600
but here's something okay why is this

530
00:19:43,590 --> 00:19:41,120
term here

531
00:19:44,310 --> 00:19:43,600
okay look over here so mu is over here

532
00:19:46,150 --> 00:19:44,320
to

533
00:19:49,190 --> 00:19:46,160
maintain the fluctuation dissipation

534
00:19:51,750 --> 00:19:49,200
theorem but now mu keeps changing

535
00:19:53,190 --> 00:19:51,760
in time it's actually also a stochastic

536
00:19:55,510 --> 00:19:53,200
variable now

537
00:19:58,070 --> 00:19:55,520
so this is very complicated took a long

538
00:20:00,390 --> 00:19:58,080
time to figure out

539
00:20:02,870 --> 00:20:00,400
what's happening is we have a noisy term

540
00:20:04,549 --> 00:20:02,880
mu times that thermal force which we

541
00:20:07,430 --> 00:20:04,559
know is noisy that gives us

542
00:20:09,510 --> 00:20:07,440
multiplicative noise that's extra noise

543
00:20:12,230 --> 00:20:09,520
it's complicated

544
00:20:14,470 --> 00:20:12,240
now you can you have to correct for that

545
00:20:16,870 --> 00:20:14,480
to maintain the fluctuation dissipation

546
00:20:19,110 --> 00:20:16,880
theorem it's a non-linear effect and

547
00:20:21,430 --> 00:20:19,120
that's what gives us this term

548
00:20:23,909 --> 00:20:21,440
so this drift current is ensure is

549
00:20:26,149 --> 00:20:23,919
basically ensuring that there's no net

550
00:20:27,990 --> 00:20:26,159
occurring a current flowing at any

551
00:20:32,710 --> 00:20:28,000
temperature basically we achieve

552
00:20:36,230 --> 00:20:34,310
it's because of this multiplicative

553
00:20:38,710 --> 00:20:36,240
noise we've got to correct for this here

554
00:20:41,669 --> 00:20:38,720
it's an exact correction

555
00:20:43,990 --> 00:20:41,679
but here we find a hint that we might be

556
00:20:46,149 --> 00:20:44,000
successful in energy harvesting so if we

557
00:20:48,149 --> 00:20:46,159
look at the steady state that is if d if

558
00:20:50,549 --> 00:20:48,159
i goes to zero if the current stops

559
00:20:52,149 --> 00:20:50,559
flowing that's the steady state solution

560
00:20:53,270 --> 00:20:52,159
up here

561
00:20:55,350 --> 00:20:53,280
this term

562
00:20:57,110 --> 00:20:55,360
this voltage

563
00:21:00,149 --> 00:20:57,120
can't be zero it needs to equal this

564
00:21:03,270 --> 00:21:00,159
term so we have a voltage

565
00:21:05,750 --> 00:21:03,280
that must be present in the diode

566
00:21:07,590 --> 00:21:05,760
at some temperature t

567
00:21:09,110 --> 00:21:07,600
so that voltage is non-zero that's

568
00:21:13,510 --> 00:21:09,120
giving us a hint that we're going to

569
00:21:17,669 --> 00:21:14,870
all right let me just chat about the

570
00:21:19,830 --> 00:21:17,679
diodes real quick we do need diodes they

571
00:21:23,110 --> 00:21:19,840
have to be real diodes that that means

572
00:21:25,270 --> 00:21:23,120
they have to be leaky diodes

573
00:21:28,710 --> 00:21:25,280
for convenience we parameterize the

574
00:21:30,070 --> 00:21:28,720
diodes with um a sigmoid function which

575
00:21:31,830 --> 00:21:30,080
is what this is so this is the

576
00:21:33,430 --> 00:21:31,840
conductance

577
00:21:35,510 --> 00:21:33,440
the only parameter here which is

578
00:21:38,950 --> 00:21:35,520
convenient is u0

579
00:21:41,590 --> 00:21:38,960
if u0 is set equal to 0 it's called a

580
00:21:44,630 --> 00:21:41,600
perfect diode it'll have no conductance

581
00:21:46,710 --> 00:21:44,640
in reverse bias and it'll be a perfect

582
00:21:48,070 --> 00:21:46,720
have perfect unity conductance and

583
00:21:50,870 --> 00:21:48,080
forward bias

584
00:21:53,430 --> 00:21:50,880
so it's controlling the leakiness

585
00:21:55,110 --> 00:21:53,440
if we let u zero become really large

586
00:21:58,070 --> 00:21:55,120
then the conductance flattens out in

587
00:22:00,310 --> 00:21:58,080
fact it turns into a resistor

588
00:22:01,750 --> 00:22:00,320
here's some iv characteristics you can

589
00:22:03,430 --> 00:22:01,760
see that they're leaking they're

590
00:22:05,350 --> 00:22:03,440
non-ideal

591
00:22:07,029 --> 00:22:05,360
i mentioned that mu the rate of change

592
00:22:10,230 --> 00:22:07,039
in mu is important so i'm just plotting

593
00:22:13,350 --> 00:22:10,240
that here as u0 gets smaller this

594
00:22:18,470 --> 00:22:13,360
derivative gets larger and larger

595
00:22:22,710 --> 00:22:20,390
all right so here's the full system

596
00:22:24,390 --> 00:22:22,720
sorry i have a lot of math here

597
00:22:26,390 --> 00:22:24,400
the ito longevity equations with

598
00:22:27,990 --> 00:22:26,400
kirchhoff's laws so let's write down

599
00:22:29,909 --> 00:22:28,000
kirchhoff's loop laws i'll just point

600
00:22:31,830 --> 00:22:29,919
them out to you basically there's two

601
00:22:34,390 --> 00:22:31,840
loops in this circuit there's a diode

602
00:22:36,310 --> 00:22:34,400
one c one to the capacitor

603
00:22:38,549 --> 00:22:36,320
there's the kirchhoff's there's the

604
00:22:40,470 --> 00:22:38,559
diode voltage right here it's going to

605
00:22:44,230 --> 00:22:40,480
be this voltage plus this voltage we're

606
00:22:46,230 --> 00:22:44,240
going to let v equal zero from that one

607
00:22:48,390 --> 00:22:46,240
and then the other loop is going through

608
00:22:50,070 --> 00:22:48,400
the second diode the second capacitor

609
00:22:51,830 --> 00:22:50,080
and then the graphene okay so those are

610
00:22:53,750 --> 00:22:51,840
the two loops

611
00:22:55,990 --> 00:22:53,760
we also have a kirchhoff's junction law

612
00:22:58,470 --> 00:22:56,000
so any current that's coming from the

613
00:23:00,630 --> 00:22:58,480
graphene hits this junction

614
00:23:02,470 --> 00:23:00,640
and gets split so there's an i1 goes

615
00:23:04,789 --> 00:23:02,480
this way and i2 goes this way and they

616
00:23:06,710 --> 00:23:04,799
have to add up to i

617
00:23:08,710 --> 00:23:06,720
if we set all the initial charges on

618
00:23:11,190 --> 00:23:08,720
these three capacitors to zero we can

619
00:23:13,110 --> 00:23:11,200
rewrite this junction law is just q is

620
00:23:14,710 --> 00:23:13,120
q1 plus q2

621
00:23:16,470 --> 00:23:14,720
what i want to point out here just to

622
00:23:18,630 --> 00:23:16,480
give you a little force for the little

623
00:23:21,750 --> 00:23:18,640
foreshadowing

624
00:23:25,110 --> 00:23:21,760
there this is an algebraic constraint

625
00:23:27,590 --> 00:23:25,120
it's just conservation laws imposed on

626
00:23:30,310 --> 00:23:27,600
our stochastic equations these will have

627
00:23:32,149 --> 00:23:30,320
profound consequences we'll see

628
00:23:34,149 --> 00:23:32,159
so here's our three

629
00:23:36,070 --> 00:23:34,159
differential equation or this is the

630
00:23:38,149 --> 00:23:36,080
brownian motion for the graphene i added

631
00:23:39,990 --> 00:23:38,159
one more term since the graphene's near

632
00:23:41,990 --> 00:23:40,000
the electrode and it can have charge on

633
00:23:44,789 --> 00:23:42,000
it there's a coulomb interaction

634
00:23:46,630 --> 00:23:44,799
this q is stochastic and we square it so

635
00:23:49,590 --> 00:23:46,640
there's more multiplicative noise here

636
00:23:51,830 --> 00:23:49,600
it's very complicated

637
00:23:53,510 --> 00:23:51,840
there's the two differential equations

638
00:23:55,430 --> 00:23:53,520
for the current

639
00:23:57,510 --> 00:23:55,440
i is one and two here those are the same

640
00:24:00,470 --> 00:23:57,520
as i wrote down before so in the end we

641
00:24:01,669 --> 00:24:00,480
have three couple stochastic non-linear

642
00:24:03,830 --> 00:24:01,679
stiff

643
00:24:05,990 --> 00:24:03,840
differential equations they have to be

644
00:24:08,390 --> 00:24:06,000
solved numerically give a little shout

645
00:24:10,630 --> 00:24:08,400
out to uh mathematic here for the

646
00:24:13,750 --> 00:24:10,640
earlier talk this week i recommend using

647
00:24:15,590 --> 00:24:13,760
mathematica to solve these

648
00:24:18,549 --> 00:24:15,600
look we're going to look for solutions

649
00:24:20,230 --> 00:24:18,559
very far from equilibrium you have to do

650
00:24:22,230 --> 00:24:20,240
it numerically

651
00:24:25,909 --> 00:24:22,240
there's actually a very large parameter

652
00:24:28,310 --> 00:24:25,919
space here it took us 1.5 years now to

653
00:24:30,630 --> 00:24:28,320
study this parameter space we just

654
00:24:32,549 --> 00:24:30,640
wrapped this up we've been using a

655
00:24:35,269 --> 00:24:32,559
supercomputer

656
00:24:37,830 --> 00:24:35,279
we have 10 billion time steps for each

657
00:24:40,470 --> 00:24:37,840
simulation and each one we do with 3 000

658
00:24:44,950 --> 00:24:40,480
realizations and a huge parameter space

659
00:24:49,909 --> 00:24:47,510
so here's our surprise discovery

660
00:24:53,110 --> 00:24:49,919
charge is added to capacitors 1 and

661
00:24:55,110 --> 00:24:53,120
capacitor 2 and energy is harvested

662
00:24:57,350 --> 00:24:55,120
here's a plot showing the charge on all

663
00:24:59,110 --> 00:24:57,360
three capacitors in time

664
00:25:00,950 --> 00:24:59,120
let's start with the blue one the blue

665
00:25:03,110 --> 00:25:00,960
one is the graphene

666
00:25:05,669 --> 00:25:03,120
the graphene doesn't build up any charge

667
00:25:07,430 --> 00:25:05,679
well mostly the voltage is set to zero

668
00:25:08,870 --> 00:25:07,440
so that's going to keep the charge here

669
00:25:10,070 --> 00:25:08,880
at zero

670
00:25:11,750 --> 00:25:10,080
and so it

671
00:25:13,510 --> 00:25:11,760
just fluctuates a little bit and stays

672
00:25:17,029 --> 00:25:13,520
zero the whole time but look at this

673
00:25:19,830 --> 00:25:17,039
green one the charge rises quite quickly

674
00:25:23,269 --> 00:25:19,840
and reaches a steady state close to 20.

675
00:25:25,590 --> 00:25:23,279
this is q2 so this is the charge on c2

676
00:25:27,510 --> 00:25:25,600
the red one is decreasing had building

677
00:25:29,510 --> 00:25:27,520
up a negative charge on it so it gets to

678
00:25:31,909 --> 00:25:29,520
about negative 20 and reaches a steady

679
00:25:34,549 --> 00:25:31,919
state that's c1

680
00:25:38,230 --> 00:25:34,559
notice that q1 and q2 are strongly

681
00:25:40,549 --> 00:25:38,240
anti-correlated anywhere q1 goes q2 has

682
00:25:42,789 --> 00:25:40,559
to do the opposite there's a strong

683
00:25:45,750 --> 00:25:42,799
anti-correlation here this is coming

684
00:25:47,990 --> 00:25:45,760
about because of kirchhoff's laws

685
00:25:50,149 --> 00:25:48,000
so how can this circuit harvest energy

686
00:25:52,390 --> 00:25:50,159
from the thermal environment

687
00:25:54,070 --> 00:25:52,400
there's three ingredients we believe are

688
00:25:56,549 --> 00:25:54,080
needed

689
00:25:58,470 --> 00:25:56,559
the graphene which is the very c of x

690
00:26:00,789 --> 00:25:58,480
capacitor we need it to be much much

691
00:26:03,029 --> 00:26:00,799
smaller than the storage capacitors this

692
00:26:05,190 --> 00:26:03,039
boosts the voltage to really high levels

693
00:26:08,390 --> 00:26:05,200
for the diodes

694
00:26:09,590 --> 00:26:08,400
the diodes generate multiplicative noise

695
00:26:12,070 --> 00:26:09,600
i pointed that out to you there's

696
00:26:14,230 --> 00:26:12,080
multiplicative noise in diodes that

697
00:26:15,909 --> 00:26:14,240
shifts the voltage the diode voltage

698
00:26:18,070 --> 00:26:15,919
away from zero so we can have a

699
00:26:20,470 --> 00:26:18,080
persistent voltage

700
00:26:21,269 --> 00:26:20,480
we also need this junction

701
00:26:23,430 --> 00:26:21,279
here

702
00:26:25,590 --> 00:26:23,440
the junction in fact the junction has to

703
00:26:26,950 --> 00:26:25,600
be followed by diodes wired in

704
00:26:28,710 --> 00:26:26,960
opposition

705
00:26:30,789 --> 00:26:28,720
we've run the simulations with the

706
00:26:32,950 --> 00:26:30,799
diodes oriented in the same direction

707
00:26:35,110 --> 00:26:32,960
you can't harvest energy then

708
00:26:38,549 --> 00:26:35,120
we've also cut off this loop if you

709
00:26:39,510 --> 00:26:38,559
force q2 to go to zero then q1 goes to

710
00:26:41,269 --> 00:26:39,520
0.

711
00:26:42,390 --> 00:26:41,279
you need these two loops you need the

712
00:26:44,230 --> 00:26:42,400
junction

713
00:26:45,269 --> 00:26:44,240
you can kind of see that here we have

714
00:26:48,470 --> 00:26:45,279
that q

715
00:26:51,590 --> 00:26:48,480
is equal to q1 plus q2 if we look at the

716
00:26:54,230 --> 00:26:51,600
time averages or ensemble averages

717
00:26:56,630 --> 00:26:54,240
we know q is zero so that says that q1

718
00:26:58,710 --> 00:26:56,640
is negative of q2

719
00:27:00,630 --> 00:26:58,720
if we square this thing let's kind of

720
00:27:03,590 --> 00:27:00,640
talk about the energy

721
00:27:06,950 --> 00:27:03,600
q1 squared plus q2 squared is going to

722
00:27:08,870 --> 00:27:06,960
be q squared minus 2q1 this is a

723
00:27:11,190 --> 00:27:08,880
correlation function here really between

724
00:27:13,269 --> 00:27:11,200
these stochastic variables

725
00:27:15,430 --> 00:27:13,279
we can see q1 squared

726
00:27:17,909 --> 00:27:15,440
it's just negative 20 times negative 20.

727
00:27:19,590 --> 00:27:17,919
it's 400 q2 squared

728
00:27:21,190 --> 00:27:19,600
is also 400

729
00:27:23,590 --> 00:27:21,200
q squared is zero

730
00:27:26,190 --> 00:27:23,600
and then minus two this is q1 times it's

731
00:27:29,110 --> 00:27:26,200
20 times negative 20. so we the the

732
00:27:31,350 --> 00:27:29,120
anticorrelation of q1 and q2 is driving

733
00:27:34,470 --> 00:27:31,360
the energy harvesting it's responsible

734
00:27:37,830 --> 00:27:34,480
for it you can see that here

735
00:27:41,350 --> 00:27:37,840
let's look at the ensemble averages

736
00:27:47,269 --> 00:27:44,789
if you plot the capacitor charge

737
00:27:50,389 --> 00:27:47,279
as a function of capacitance the storage

738
00:27:53,510 --> 00:27:50,399
capacitors capacitance

739
00:27:55,510 --> 00:27:53,520
you we find that you'll store more

740
00:27:57,909 --> 00:27:55,520
charge if you have a bigger capacitor in

741
00:27:59,430 --> 00:27:57,919
fact it's linearly precisely linear in

742
00:28:01,110 --> 00:27:59,440
that what does that mean it means

743
00:28:03,350 --> 00:28:01,120
they're all being charged to the same

744
00:28:05,669 --> 00:28:03,360
voltage the same that's that diode

745
00:28:07,750 --> 00:28:05,679
voltage i pointed out there's some diode

746
00:28:09,510 --> 00:28:07,760
persistent diode voltage which be it's

747
00:28:11,830 --> 00:28:09,520
being held here

748
00:28:14,230 --> 00:28:11,840
now let's look at the diode parameter

749
00:28:15,909 --> 00:28:14,240
turns out you can maximize the charge

750
00:28:18,950 --> 00:28:15,919
stored on the capacitor if the diode

751
00:28:21,110 --> 00:28:18,960
parameter is about 0.15 and very

752
00:28:23,510 --> 00:28:21,120
interestingly if the diode parameter

753
00:28:26,149 --> 00:28:23,520
gets smaller and smaller we follow this

754
00:28:28,630 --> 00:28:26,159
all the way to zero it goes to zero it's

755
00:28:31,110 --> 00:28:28,640
exactly zero if you have a perfect diode

756
00:28:33,029 --> 00:28:31,120
you can't harvest energy

757
00:28:35,029 --> 00:28:33,039
on the flip side if the diode primer

758
00:28:36,630 --> 00:28:35,039
gets larger and larger it also goes to

759
00:28:38,710 --> 00:28:36,640
zero that's because it turns into a

760
00:28:41,029 --> 00:28:38,720
resistor so you can't harvest energy

761
00:28:43,029 --> 00:28:41,039
with resistor

762
00:28:45,110 --> 00:28:43,039
if you look at the ensemble averages in

763
00:28:47,430 --> 00:28:45,120
the capacitor charge that earlier one

764
00:28:48,870 --> 00:28:47,440
was one realization so we do 3000

765
00:28:51,590 --> 00:28:48,880
realizations

766
00:28:54,310 --> 00:28:51,600
you get these nice smooth capacitor

767
00:28:57,750 --> 00:28:54,320
charge versus time curves in fact

768
00:29:00,950 --> 00:28:57,760
they're exactly rc charging circuits

769
00:29:03,669 --> 00:29:00,960
if you look at the time constant tau of

770
00:29:05,510 --> 00:29:03,679
the rc circuit which is r times c it's

771
00:29:07,750 --> 00:29:05,520
perfectly linear

772
00:29:09,909 --> 00:29:07,760
in capacitance

773
00:29:12,630 --> 00:29:09,919
so it's exactly like the rc charging

774
00:29:14,470 --> 00:29:12,640
which i showed you in the deterministic

775
00:29:16,549 --> 00:29:14,480
so then we can look at the charge the

776
00:29:19,029 --> 00:29:16,559
voltage the current and the power as a

777
00:29:21,029 --> 00:29:19,039
function of time so here's the capacitor

778
00:29:23,029 --> 00:29:21,039
charge charging up

779
00:29:24,549 --> 00:29:23,039
that allows us to determine the voltage

780
00:29:26,789 --> 00:29:24,559
on the capacitor

781
00:29:28,230 --> 00:29:26,799
it's rate it's continuously rising we

782
00:29:30,549 --> 00:29:28,240
can also get the current so see the

783
00:29:32,470 --> 00:29:30,559
current starts high and then decays

784
00:29:34,070 --> 00:29:32,480
exponentially in time

785
00:29:35,750 --> 00:29:34,080
if you take the current times the

786
00:29:37,510 --> 00:29:35,760
voltage you'll get the power look

787
00:29:39,190 --> 00:29:37,520
there's a peak power remember i

788
00:29:41,510 --> 00:29:39,200
mentioned the peak power this circuit

789
00:29:45,190 --> 00:29:41,520
has 50 efficiency there's the peak

790
00:29:50,870 --> 00:29:46,950
all right can we find can we really find

791
00:29:52,630 --> 00:29:50,880
the source of energy we can in fact

792
00:29:55,190 --> 00:29:52,640
using what's called stochastic

793
00:29:57,269 --> 00:29:55,200
thermodynamics this is an emergent field

794
00:29:59,590 --> 00:29:57,279
of physics honestly with low hanging

795
00:30:01,430 --> 00:29:59,600
fruit you know anything we look at never

796
00:30:04,549 --> 00:30:01,440
been seen before

797
00:30:05,830 --> 00:30:04,559
is revealing a lot of nice things so

798
00:30:09,190 --> 00:30:05,840
basically

799
00:30:10,789 --> 00:30:09,200
it allows us to look intimately at all

800
00:30:12,389 --> 00:30:10,799
the sources of

801
00:30:14,230 --> 00:30:12,399
energy

802
00:30:16,149 --> 00:30:14,240
heat and work

803
00:30:19,110 --> 00:30:16,159
so here's the graphene

804
00:30:22,230 --> 00:30:19,120
heat bath we can track the we can track

805
00:30:25,590 --> 00:30:22,240
what it's doing here's the graphing uh

806
00:30:28,470 --> 00:30:25,600
drag the resistance basically the losses

807
00:30:32,149 --> 00:30:28,480
there's the resistor dissipated power

808
00:30:33,750 --> 00:30:32,159
and there's the resistors heat valve

809
00:30:34,950 --> 00:30:33,760
so what we do is we write down the

810
00:30:36,950 --> 00:30:34,960
energy of the system that's

811
00:30:39,350 --> 00:30:36,960
straightforward we use the first law of

812
00:30:41,350 --> 00:30:39,360
thermodynamics says the energy is the

813
00:30:43,750 --> 00:30:41,360
heat plus the work and then we go ahead

814
00:30:45,029 --> 00:30:43,760
and we calculate the heat from the point

815
00:30:46,549 --> 00:30:45,039
of view of the graphene you have to pick

816
00:30:49,350 --> 00:30:46,559
some point of view

817
00:30:50,870 --> 00:30:49,360
the heat flux produced by friction

818
00:30:52,630 --> 00:30:50,880
is this for me and these are these two

819
00:30:54,230 --> 00:30:52,640
terms over here

820
00:30:56,630 --> 00:30:54,240
those in fact

821
00:30:57,509 --> 00:30:56,640
um during the energy harvesting phase

822
00:30:59,909 --> 00:30:57,519
we've

823
00:31:01,830 --> 00:30:59,919
calculated those precisely there's there

824
00:31:04,389 --> 00:31:01,840
this is zero there's no heat there's no

825
00:31:06,149 --> 00:31:04,399
heat flux produced by graphene

826
00:31:08,230 --> 00:31:06,159
it turns out the work so this term here

827
00:31:11,110 --> 00:31:08,240
is zero so all of the energy is coming

828
00:31:13,190 --> 00:31:11,120
from the work well the work done on the

829
00:31:14,950 --> 00:31:13,200
graphene by the circuit that's given by

830
00:31:16,470 --> 00:31:14,960
this a little bit complicated and you

831
00:31:18,950 --> 00:31:16,480
can't write it analytically but it's

832
00:31:20,389 --> 00:31:18,960
close to this term this kbt over rc

833
00:31:22,630 --> 00:31:20,399
that's the power

834
00:31:25,509 --> 00:31:22,640
of the thermal bath

835
00:31:27,350 --> 00:31:25,519
being put into the diode basically and

836
00:31:29,669 --> 00:31:27,360
this is the

837
00:31:31,509 --> 00:31:29,679
dissipated power by the diode well

838
00:31:33,430 --> 00:31:31,519
here's what happens during the energy

839
00:31:35,590 --> 00:31:33,440
harvesting phase while the capacitors

840
00:31:37,909 --> 00:31:35,600
are charging up this term

841
00:31:39,509 --> 00:31:37,919
the thermal power coming from the

842
00:31:42,149 --> 00:31:39,519
thermal bath

843
00:31:44,710 --> 00:31:42,159
is slightly bigger than the dissipated

844
00:31:47,110 --> 00:31:44,720
power of the diodes and that extra

845
00:31:50,310 --> 00:31:47,120
energy charges the capacitor so that's

846
00:31:52,710 --> 00:31:50,320
the source of power we can prove that

847
00:31:54,549 --> 00:31:52,720
here's a graph of that

848
00:31:57,190 --> 00:31:54,559
so the red line here

849
00:31:59,190 --> 00:31:57,200
these all start at zero but the red line

850
00:32:00,870 --> 00:31:59,200
is the energy of the system so this is

851
00:32:02,870 --> 00:32:00,880
the charging of the capacitors of course

852
00:32:04,710 --> 00:32:02,880
they're storing energy so their energy

853
00:32:07,669 --> 00:32:04,720
is changing in time

854
00:32:09,590 --> 00:32:07,679
the green one is the work plus the heat

855
00:32:11,110 --> 00:32:09,600
but we also separately check the heat

856
00:32:12,470 --> 00:32:11,120
it's actually zero so this is really

857
00:32:15,430 --> 00:32:12,480
just the work

858
00:32:17,269 --> 00:32:15,440
if you subtract these two

859
00:32:18,870 --> 00:32:17,279
they're basically always zero there's

860
00:32:20,230 --> 00:32:18,880
this is actually it's numerically

861
00:32:22,230 --> 00:32:20,240
challenging there's some slight

862
00:32:24,389 --> 00:32:22,240
numerical drift here that's happening in

863
00:32:26,710 --> 00:32:24,399
time which we've worked very hard to

864
00:32:29,669 --> 00:32:26,720
deal with but notice how this hairiness

865
00:32:32,149 --> 00:32:29,679
goes away this tells us the first law is

866
00:32:34,149 --> 00:32:32,159
rigorously obeyed at every time step

867
00:32:36,230 --> 00:32:34,159
this is what this is telling us so we

868
00:32:39,029 --> 00:32:36,240
are satisfying the law the first law of

869
00:32:41,669 --> 00:32:39,039
physics which is here

870
00:32:44,789 --> 00:32:41,679
so energy is increasing in time as the

871
00:32:47,110 --> 00:32:44,799
capacitors charge up so h is growing

872
00:32:49,509 --> 00:32:47,120
graphing does not provide an energy q is

873
00:32:51,509 --> 00:32:49,519
zero the power comes from the thermal

874
00:32:53,590 --> 00:32:51,519
bath of the diode so the work done is

875
00:32:55,909 --> 00:32:53,600
what's giving us the energy

876
00:32:57,990 --> 00:32:55,919
the graphene does provide the voltage

877
00:32:59,990 --> 00:32:58,000
though at these top rails so this is a

878
00:33:02,070 --> 00:33:00,000
very interesting thing

879
00:33:04,470 --> 00:33:02,080
why you need these two loops

880
00:33:07,269 --> 00:33:04,480
so current actually flows

881
00:33:09,029 --> 00:33:07,279
between the diodes basically forming a

882
00:33:11,430 --> 00:33:09,039
vortex here

883
00:33:14,070 --> 00:33:11,440
the circulating current is here charging

884
00:33:16,149 --> 00:33:14,080
one positive the other negative

885
00:33:18,070 --> 00:33:16,159
and all the power and the current is

886
00:33:20,310 --> 00:33:18,080
here even though the voltage is set by

887
00:33:22,710 --> 00:33:20,320
this guy over here along these top rails

888
00:33:24,470 --> 00:33:22,720
again v is zero here

889
00:33:25,669 --> 00:33:24,480
very interesting all right what about

890
00:33:28,310 --> 00:33:25,679
the entry

891
00:33:30,710 --> 00:33:28,320
the measure of disorder we can track the

892
00:33:32,470 --> 00:33:30,720
entropy during charging using the shin

893
00:33:34,070 --> 00:33:32,480
and entropy formula basically looks at

894
00:33:37,190 --> 00:33:34,080
the probability

895
00:33:38,710 --> 00:33:37,200
of having a certain charge in time

896
00:33:40,549 --> 00:33:38,720
all right so we have those three

897
00:33:42,230 --> 00:33:40,559
thousand realizations so everything's

898
00:33:43,269 --> 00:33:42,240
the same except the random numbers

899
00:33:45,269 --> 00:33:43,279
change

900
00:33:47,590 --> 00:33:45,279
we always start with q equals zero and

901
00:33:49,990 --> 00:33:47,600
then we track q1 and q2 in time just

902
00:33:51,909 --> 00:33:50,000
like the graph showed before

903
00:33:54,389 --> 00:33:51,919
and then we find the probability of

904
00:33:56,950 --> 00:33:54,399
having a specific set of charges q1 and

905
00:33:57,909 --> 00:33:56,960
q2 at a specific time

906
00:33:59,830 --> 00:33:57,919
all right

907
00:34:01,590 --> 00:33:59,840
so here's the graph of the entropy it

908
00:34:03,990 --> 00:34:01,600
starts off at zero i'll explain that in

909
00:34:06,870 --> 00:34:04,000
a second but then jumps fairly quickly

910
00:34:08,790 --> 00:34:06,880
to around four there's a slight decay in

911
00:34:11,190 --> 00:34:08,800
the entropy here we should chat about

912
00:34:13,430 --> 00:34:11,200
that maybe daniel might check on that

913
00:34:16,310 --> 00:34:13,440
uh but anyhow there's an overall

914
00:34:18,629 --> 00:34:16,320
positive production entropy from zero to

915
00:34:20,230 --> 00:34:18,639
four entropy is produced here

916
00:34:22,950 --> 00:34:20,240
at t equals zero let's see what's going

917
00:34:25,669 --> 00:34:22,960
on there so the initial conditions are

918
00:34:27,750 --> 00:34:25,679
that uh there's everything set to zero

919
00:34:29,109 --> 00:34:27,760
so for every simulation they all have

920
00:34:31,270 --> 00:34:29,119
the same initial conditions whatever

921
00:34:33,990 --> 00:34:31,280
that doesn't matter so there's a hundred

922
00:34:36,470 --> 00:34:34,000
percent probability of having the same

923
00:34:38,790 --> 00:34:36,480
initial condition and the log here which

924
00:34:40,950 --> 00:34:38,800
comes in here the log of one is zero so

925
00:34:43,030 --> 00:34:40,960
the entropy starts off at zero and it's

926
00:34:44,230 --> 00:34:43,040
positive we have a positive production

927
00:34:47,109 --> 00:34:44,240
of entropy

928
00:34:49,109 --> 00:34:47,119
so we're happy with that

929
00:34:51,190 --> 00:34:49,119
all right let me just throw some i got a

930
00:34:53,030 --> 00:34:51,200
lot of email get lots of questions let

931
00:34:54,550 --> 00:34:53,040
me just guess some questions and throw

932
00:34:56,869 --> 00:34:54,560
out some answers here

933
00:34:59,589 --> 00:34:56,879
does our energy harvesting system

934
00:35:00,550 --> 00:34:59,599
violate the first law of thermodynamics

935
00:35:03,430 --> 00:35:00,560
no

936
00:35:04,470 --> 00:35:03,440
the energy is equal to the heat plus the

937
00:35:06,790 --> 00:35:04,480
work

938
00:35:09,750 --> 00:35:06,800
that's the first law actually we found

939
00:35:14,710 --> 00:35:09,760
the heat is zero so all the work

940
00:35:18,069 --> 00:35:16,790
where does the stored capacitor energy

941
00:35:19,430 --> 00:35:18,079
come from

942
00:35:21,750 --> 00:35:19,440
well it comes from the thermal

943
00:35:24,390 --> 00:35:21,760
surroundings it's coming from this kbt

944
00:35:26,150 --> 00:35:24,400
over r c so it's the thermal it's the

945
00:35:27,829 --> 00:35:26,160
environment the thermal environment

946
00:35:29,430 --> 00:35:27,839
stealing energy from that massive

947
00:35:31,030 --> 00:35:29,440
thermal environment that daniel talked

948
00:35:32,710 --> 00:35:31,040
about

949
00:35:34,950 --> 00:35:32,720
is work done at thermodynamic

950
00:35:37,589 --> 00:35:34,960
equilibrium no our system's not in

951
00:35:39,030 --> 00:35:37,599
thermodynamic the charges are always

952
00:35:41,030 --> 00:35:39,040
moving they're always adding and

953
00:35:43,430 --> 00:35:41,040
removing

954
00:35:45,990 --> 00:35:43,440
from the system it's actually very far

955
00:35:48,470 --> 00:35:46,000
from equilibrium

956
00:35:50,710 --> 00:35:48,480
is it is useful work done at a single

957
00:35:52,470 --> 00:35:50,720
temperature yes everything's at the same

958
00:35:53,430 --> 00:35:52,480
temperature we ensured that through

959
00:35:57,270 --> 00:35:53,440
those

960
00:35:58,710 --> 00:35:57,280
you

961
00:36:00,069 --> 00:35:58,720
does our system violate the second law

962
00:36:03,030 --> 00:36:00,079
of thermodynamics

963
00:36:05,190 --> 00:36:03,040
no our system starts from equilibrium

964
00:36:07,109 --> 00:36:05,200
sorry far from equilibrium

965
00:36:09,190 --> 00:36:07,119
and is driven to a steady state by

966
00:36:10,950 --> 00:36:09,200
unbalanced forces i'll give a good

967
00:36:12,950 --> 00:36:10,960
example of this in a second those

968
00:36:15,910 --> 00:36:12,960
unbalanced forces this is the diode

969
00:36:18,069 --> 00:36:15,920
voltage it turns out that extra term

970
00:36:19,030 --> 00:36:18,079
is driving it

971
00:36:21,349 --> 00:36:19,040
is

972
00:36:23,910 --> 00:36:21,359
entropy produced yes the capacitor

973
00:36:26,069 --> 00:36:23,920
entropy increases from zero to four

974
00:36:27,990 --> 00:36:26,079
are there any pedagogical examples of

975
00:36:29,349 --> 00:36:28,000
thermal work being done at a single

976
00:36:32,470 --> 00:36:29,359
temperature

977
00:36:34,230 --> 00:36:32,480
yes as a framework consider the ideal

978
00:36:37,109 --> 00:36:34,240
gas which daniel talked about this is

979
00:36:39,349 --> 00:36:37,119
very helpful for this talk

980
00:36:41,510 --> 00:36:39,359
so here let consider work and entropy

981
00:36:43,670 --> 00:36:41,520
during an isothermal expansion so

982
00:36:44,790 --> 00:36:43,680
imagine two masses sitting on this

983
00:36:47,430 --> 00:36:44,800
balloon

984
00:36:48,550 --> 00:36:47,440
we're going to remove the first mass

985
00:36:50,230 --> 00:36:48,560
and as the

986
00:36:52,310 --> 00:36:50,240
mass gets removed the balloon can kind

987
00:36:53,589 --> 00:36:52,320
of expand because the weight's been

988
00:36:55,190 --> 00:36:53,599
removed

989
00:36:56,150 --> 00:36:55,200
and we're going to analyze

990
00:36:58,470 --> 00:36:56,160
the

991
00:37:00,230 --> 00:36:58,480
work done on this second mass as it's

992
00:37:01,589 --> 00:37:00,240
raised up a height h

993
00:37:03,430 --> 00:37:01,599
we're going to have a heater here we'll

994
00:37:05,270 --> 00:37:03,440
see we need to have that so this is to

995
00:37:07,430 --> 00:37:05,280
keep the temperature fixed

996
00:37:09,829 --> 00:37:07,440
we have uh before and after pictures

997
00:37:12,310 --> 00:37:09,839
here let's apply the first law to the

998
00:37:14,550 --> 00:37:12,320
second mass here this one

999
00:37:16,470 --> 00:37:14,560
here's the first law the heat there's no

1000
00:37:18,950 --> 00:37:16,480
heat change in this mass

1001
00:37:21,589 --> 00:37:18,960
the energy change because it was raised

1002
00:37:24,150 --> 00:37:21,599
mgh and the work was done the normal

1003
00:37:26,790 --> 00:37:24,160
force of the balloon pushed it

1004
00:37:29,670 --> 00:37:26,800
for a distance h so work was done on the

1005
00:37:31,750 --> 00:37:29,680
mass and the energy increased from that

1006
00:37:34,150 --> 00:37:31,760
this is exactly what i was saying in our

1007
00:37:36,710 --> 00:37:34,160
situation so work was done

1008
00:37:38,950 --> 00:37:36,720
by the thermal environment on the

1009
00:37:40,790 --> 00:37:38,960
capacitors or on the circuit if you like

1010
00:37:42,550 --> 00:37:40,800
and it raised its energy and the heat

1011
00:37:43,829 --> 00:37:42,560
was there was no heat change this is the

1012
00:37:45,750 --> 00:37:43,839
same as ours

1013
00:37:47,589 --> 00:37:45,760
now let's analyze the gas this is the

1014
00:37:50,310 --> 00:37:47,599
thermal gas

1015
00:37:52,710 --> 00:37:50,320
so here we know for an ideal gas that

1016
00:37:55,109 --> 00:37:52,720
the work done in an isothermal process

1017
00:37:57,430 --> 00:37:55,119
is given by this formula now here the

1018
00:37:58,630 --> 00:37:57,440
work is done by the gas so the work's

1019
00:38:01,430 --> 00:37:58,640
negative

1020
00:38:03,349 --> 00:38:01,440
let's apply the first law to the gas

1021
00:38:05,430 --> 00:38:03,359
here is the first law there's no

1022
00:38:07,750 --> 00:38:05,440
internal energy to this gas so it's

1023
00:38:09,750 --> 00:38:07,760
ideal so we're going to let h be zero so

1024
00:38:11,670 --> 00:38:09,760
that means that delta q

1025
00:38:14,870 --> 00:38:11,680
is equal to minus

1026
00:38:17,910 --> 00:38:14,880
delta w or positive so that means heat

1027
00:38:19,910 --> 00:38:17,920
flows to the gas that's why we need the

1028
00:38:22,230 --> 00:38:19,920
heater so the heater heats the gas to

1029
00:38:24,069 --> 00:38:22,240
keep the temperature constant that heat

1030
00:38:26,550 --> 00:38:24,079
is positive because it's flowing into

1031
00:38:28,230 --> 00:38:26,560
the gas that means entropy is produced

1032
00:38:29,670 --> 00:38:28,240
and it's positive these are all kind of

1033
00:38:31,829 --> 00:38:29,680
these are basically

1034
00:38:34,390 --> 00:38:31,839
equal you know in some some ideal

1035
00:38:36,870 --> 00:38:34,400
circumstances

1036
00:38:38,310 --> 00:38:36,880
so yeah so that's uh for us uh this is

1037
00:38:42,069 --> 00:38:38,320
the thermal environment around the

1038
00:38:46,950 --> 00:38:44,150
all right so let me summarize

1039
00:38:48,950 --> 00:38:46,960
stochastic thermodynamics is yielding

1040
00:38:51,670 --> 00:38:48,960
quantitative insights far from

1041
00:38:54,550 --> 00:38:51,680
equilibrium

1042
00:38:56,550 --> 00:38:54,560
graphene this capacitor c of x we've

1043
00:38:58,390 --> 00:38:56,560
i've mentioned shifts the power to low

1044
00:39:00,790 --> 00:38:58,400
frequencies due to this double well this

1045
00:39:03,190 --> 00:39:00,800
has some technological value

1046
00:39:05,030 --> 00:39:03,200
the average capacitance of graphene

1047
00:39:06,550 --> 00:39:05,040
determines the voltage

1048
00:39:08,310 --> 00:39:06,560
that's kind of like the gain or the

1049
00:39:10,870 --> 00:39:08,320
bandwidth you can think of

1050
00:39:12,710 --> 00:39:10,880
if you think of the

1051
00:39:15,190 --> 00:39:12,720
impedance

1052
00:39:17,109 --> 00:39:15,200
of a circuit the imaginary part is the

1053
00:39:18,790 --> 00:39:17,119
capacitance so it can it can do

1054
00:39:20,069 --> 00:39:18,800
something like change the gain or the

1055
00:39:22,550 --> 00:39:20,079
bandwidth

1056
00:39:24,550 --> 00:39:22,560
but the current circulates between the

1057
00:39:27,349 --> 00:39:24,560
diodes that's the resistance that's the

1058
00:39:29,829 --> 00:39:27,359
real part and it's doing the work here

1059
00:39:31,829 --> 00:39:29,839
energy harvested increases in time and

1060
00:39:33,430 --> 00:39:31,839
then stops it reaches a steady state

1061
00:39:34,790 --> 00:39:33,440
it's not like some perpetual motion

1062
00:39:36,470 --> 00:39:34,800
machine it just

1063
00:39:38,390 --> 00:39:36,480
tries to it's trying to reach steady

1064
00:39:39,910 --> 00:39:38,400
state the capacitors would

1065
00:39:41,589 --> 00:39:39,920
normally in the room right now which

1066
00:39:43,510 --> 00:39:41,599
capacitors charge would be zero and

1067
00:39:45,910 --> 00:39:43,520
that's its steady state when you hook it

1068
00:39:47,109 --> 00:39:45,920
to the circuit it wants to be something

1069
00:39:49,430 --> 00:39:47,119
else

1070
00:39:51,510 --> 00:39:49,440
that's its steady state

1071
00:39:53,829 --> 00:39:51,520
the energy source is the diode's thermal

1072
00:39:54,710 --> 00:39:53,839
bath because the remember the heat was

1073
00:39:57,829 --> 00:39:54,720
zero

1074
00:39:59,349 --> 00:39:57,839
to four

1075
00:40:00,710 --> 00:39:59,359
estimates of our power density i

1076
00:40:03,349 --> 00:40:00,720
mentioned there before it's worth kind

1077
00:40:05,510 --> 00:40:03,359
of pursuing these things

1078
00:40:07,430 --> 00:40:05,520
and then let me just acknowledge pradeep

1079
00:40:09,109 --> 00:40:07,440
and saran been chatting with them for

1080
00:40:11,750 --> 00:40:09,119
years about this has been extremely

1081
00:40:14,630 --> 00:40:11,760
helpful also john new at uc berkeley and

1082
00:40:16,550 --> 00:40:14,640
louis vanilla carlos iii these guys are

1083
00:40:18,309 --> 00:40:16,560
world experts in stochastic

1084
00:40:19,910 --> 00:40:18,319
thermodynamics we couldn't move forward

1085
00:40:20,790 --> 00:40:19,920
without them

1086
00:40:23,510 --> 00:40:20,800
we are

1087
00:40:25,589 --> 00:40:23,520
summarizing this paper i hope to get it

1088
00:40:28,470 --> 00:40:25,599
on the archive before we submit it for

1089
00:40:31,109 --> 00:40:28,480
publication here in a few weeks and also

1090
00:40:33,829 --> 00:40:31,119
let me thank funding sources here

1091
00:40:34,950 --> 00:40:33,839
that i'm done thank you very much

1092
00:40:38,710 --> 00:40:34,960
thank you

1093
00:40:41,510 --> 00:40:38,720
uh what a fantastic presentation uh this

1094
00:40:44,790 --> 00:40:41,520
uh your work is so careful

1095
00:40:47,349 --> 00:40:44,800
and so fascinating um i'm sure they're

1096
00:40:49,829 --> 00:40:47,359
gonna be a lot of questions uh i'll

1097
00:40:51,030 --> 00:40:49,839
start off with a very quick one and that

1098
00:40:53,109 --> 00:40:51,040
is that you

1099
00:40:55,030 --> 00:40:53,119
have described your

1100
00:40:58,150 --> 00:40:55,040
uh

1101
00:41:01,270 --> 00:40:58,160
system as being far from equilibrium and

1102
00:41:03,670 --> 00:41:01,280
therefore not violating the second law

1103
00:41:07,270 --> 00:41:03,680
if you take your system

1104
00:41:09,670 --> 00:41:07,280
of the graphene and you just start it in

1105
00:41:11,990 --> 00:41:09,680
a thermal equilibrium

1106
00:41:14,309 --> 00:41:12,000
what nudges it to be far from

1107
00:41:17,589 --> 00:41:14,319
equilibrium if it isn't the system

1108
00:41:22,870 --> 00:41:18,630
yes

1109
00:41:27,670 --> 00:41:24,870
so for example here

1110
00:41:30,390 --> 00:41:27,680
uh once the charge has reached this

1111
00:41:34,309 --> 00:41:30,400
steady state value

1112
00:41:35,190 --> 00:41:34,319
so that is the steady state solution to

1113
00:41:39,829 --> 00:41:35,200
this

1114
00:41:42,390 --> 00:41:39,839
and

1115
00:41:45,750 --> 00:41:42,400
it's not that's not in thermodynamic

1116
00:41:47,349 --> 00:41:45,760
equilibrium but it is in a steady state

1117
00:41:49,190 --> 00:41:47,359
and if you start the system in the

1118
00:41:50,390 --> 00:41:49,200
steady state it stays in that steady

1119
00:41:52,390 --> 00:41:50,400
state

1120
00:41:54,390 --> 00:41:52,400
if you start with the capacitors with

1121
00:41:57,270 --> 00:41:54,400
more charges so you start with 100 units

1122
00:41:59,670 --> 00:41:57,280
of charge on the capacitor it will lose

1123
00:42:01,589 --> 00:41:59,680
charge until it gets down to 20. it's

1124
00:42:04,390 --> 00:42:01,599
trying to get to here

1125
00:42:07,270 --> 00:42:04,400
at this um 20 level and if you start it

1126
00:42:10,230 --> 00:42:07,280
with zero which is what we like to do

1127
00:42:11,349 --> 00:42:10,240
uh then it will rise to 20. so does that

1128
00:42:13,589 --> 00:42:11,359
answer the question that that's

1129
00:42:16,950 --> 00:42:13,599
basically what will happen yes so if you

1130
00:42:19,109 --> 00:42:16,960
start from zero from equilibrium it it

1131
00:42:22,470 --> 00:42:19,119
goes into this far from equilibrium

1132
00:42:24,470 --> 00:42:22,480
state spontaneously and if you bleed the

1133
00:42:27,030 --> 00:42:24,480
charge off say into a motor or a

1134
00:42:30,390 --> 00:42:27,040
resistor or something like that are you

1135
00:42:34,230 --> 00:42:30,400
will that happen continuously

1136
00:42:38,390 --> 00:42:34,240
yeah yeah so you could uh you know it's

1137
00:42:39,270 --> 00:42:38,400
ideal to run this type of circuit at the

1138
00:42:41,109 --> 00:42:39,280
uh

1139
00:42:43,270 --> 00:42:41,119
peak power

1140
00:42:44,790 --> 00:42:43,280
i think i have that here so here's where

1141
00:42:47,030 --> 00:42:44,800
you'd want to that'd be the operating

1142
00:42:48,710 --> 00:42:47,040
point for the circuit basically because

1143
00:42:51,109 --> 00:42:48,720
then you're drawing the most amount of

1144
00:42:53,510 --> 00:42:51,119
power from the thermal environment

1145
00:42:55,589 --> 00:42:53,520
right um and so what you would do is try

1146
00:42:59,030 --> 00:42:55,599
to hold it at that point

1147
00:43:01,349 --> 00:42:59,040
by removing current at the rate that the

1148
00:43:03,270 --> 00:43:01,359
current is coming in at so it's stuck

1149
00:43:04,390 --> 00:43:03,280
there basically and you get the most

1150
00:43:07,750 --> 00:43:04,400
efficient

1151
00:43:09,990 --> 00:43:07,760
machine at that point

1152
00:43:12,470 --> 00:43:10,000
okay uh i we will have to talk about the

1153
00:43:13,829 --> 00:43:12,480
implications

1154
00:43:14,710 --> 00:43:13,839
um

1155
00:43:16,870 --> 00:43:14,720
i think

1156
00:43:18,150 --> 00:43:16,880
schaefer is the next person shaffer has

1157
00:43:21,190 --> 00:43:18,160
the next question

1158
00:43:23,349 --> 00:43:21,200
yeah aiden schaefer um real simple

1159
00:43:25,270 --> 00:43:23,359
question on that

1160
00:43:28,870 --> 00:43:25,280
the chipset the larger chip that you

1161
00:43:33,589 --> 00:43:28,880
built was that uh an even or odd number

1162
00:43:37,589 --> 00:43:35,510
well you know we've done a whole bunch

1163
00:43:40,710 --> 00:43:37,599
of things we've made a bunch of chips

1164
00:43:42,309 --> 00:43:40,720
there it's expensive to make these shoes

1165
00:43:45,270 --> 00:43:42,319
okay

1166
00:43:47,430 --> 00:43:45,280
um we run lots of experiments on each

1167
00:43:49,589 --> 00:43:47,440
chip it turns out as well

1168
00:43:51,910 --> 00:43:49,599
so you'll find pretty much anything and

1169
00:43:54,710 --> 00:43:51,920
everything you can i i

1170
00:43:56,069 --> 00:43:54,720
i only we were only able to

1171
00:43:58,870 --> 00:43:56,079
prove

1172
00:44:01,190 --> 00:43:58,880
that if you if you have one loop here if

1173
00:44:03,670 --> 00:44:01,200
you just do a one like a half wave

1174
00:44:05,910 --> 00:44:03,680
rectifier it won't right in in the

1175
00:44:08,790 --> 00:44:05,920
thermal in the if you want to harvest

1176
00:44:10,710 --> 00:44:08,800
thermal energy it won't work it'll work

1177
00:44:12,470 --> 00:44:10,720
in the deterministic case i mean if

1178
00:44:13,270 --> 00:44:12,480
something's shaking the graphene it'll

1179
00:44:16,069 --> 00:44:13,280
work

1180
00:44:18,550 --> 00:44:16,079
but um if you want to harvest thermal

1181
00:44:23,230 --> 00:44:18,560
energy well then you need you need a

1182
00:44:23,240 --> 00:44:26,309
[Music]

1183
00:44:32,870 --> 00:44:29,990
a capacitor diode ladder filter

1184
00:44:35,270 --> 00:44:32,880
um and it only functions

1185
00:44:39,510 --> 00:44:35,280
all of the diodes are in one direction

1186
00:44:42,230 --> 00:44:39,520
but uh its job is to center a waveform

1187
00:44:45,430 --> 00:44:42,240
uh that's going through it so it's

1188
00:44:47,990 --> 00:44:45,440
this is just uh reminiscent of that but

1189
00:44:51,190 --> 00:44:48,000
you have the diodes in opposite pairs

1190
00:44:53,430 --> 00:44:51,200
for energy generation

1191
00:44:56,150 --> 00:44:53,440
right there's a there's a lot of circuit

1192
00:44:58,150 --> 00:44:56,160
topologies out there

1193
00:45:00,710 --> 00:44:58,160
and and we've played with a whole bunch

1194
00:45:02,950 --> 00:45:00,720
of them and uh you know some are like

1195
00:45:05,430 --> 00:45:02,960
like a cockroft walton generator

1196
00:45:07,109 --> 00:45:05,440
multiplier right so there's a lot of

1197
00:45:09,109 --> 00:45:07,119
really interesting

1198
00:45:12,390 --> 00:45:09,119
i kind of mentioned the low hanging

1199
00:45:13,990 --> 00:45:12,400
fruit here i mean each topology requires

1200
00:45:16,390 --> 00:45:14,000
that you go through

1201
00:45:18,470 --> 00:45:16,400
what we did in great detail

1202
00:45:20,150 --> 00:45:18,480
because they're it's hard to map from

1203
00:45:22,950 --> 00:45:20,160
one to the next

1204
00:45:26,950 --> 00:45:24,950
i think that's why double e such is its

1205
00:45:28,950 --> 00:45:26,960
own field because every topology you

1206
00:45:30,550 --> 00:45:28,960
gotta sit and take a look at it and see

1207
00:45:32,230 --> 00:45:30,560
what it's gonna do

1208
00:45:35,510 --> 00:45:32,240
okay thank you there's a lot of

1209
00:45:36,870 --> 00:45:35,520
opportunity here though yeah

1210
00:45:42,230 --> 00:45:36,880
thank you uh

1211
00:45:47,190 --> 00:45:44,710
paul thank you for just a marvelous talk

1212
00:45:50,710 --> 00:45:47,200
um really nicely explained and very

1213
00:45:51,910 --> 00:45:50,720
careful um i i'm still at a loss i mean

1214
00:45:53,589 --> 00:45:51,920
i i think i understand what you're

1215
00:45:54,710 --> 00:45:53,599
saying your system comes to a steady

1216
00:45:57,430 --> 00:45:54,720
state

1217
00:45:59,510 --> 00:45:57,440
and as it's posed

1218
00:46:01,510 --> 00:45:59,520
as far as you've gone i would agree that

1219
00:46:03,109 --> 00:46:01,520
the second law is not is not violated i

1220
00:46:05,829 --> 00:46:03,119
agree with you on that

1221
00:46:07,750 --> 00:46:05,839
however i i i don't feel you've really

1222
00:46:09,910 --> 00:46:07,760
addressed the question if if you're con

1223
00:46:12,309 --> 00:46:09,920
if you can constantly siphon off energy

1224
00:46:15,510 --> 00:46:12,319
from each of these capacitors

1225
00:46:17,510 --> 00:46:15,520
to do external work then thermodynamics

1226
00:46:19,750 --> 00:46:17,520
is pretty clear that if you're if if you

1227
00:46:21,910 --> 00:46:19,760
are turning thermal energy

1228
00:46:23,589 --> 00:46:21,920
into into the capacitive energy which

1229
00:46:25,030 --> 00:46:23,599
you're claiming and then you're using

1230
00:46:27,910 --> 00:46:25,040
that energy

1231
00:46:31,190 --> 00:46:27,920
to carry out external work and if your

1232
00:46:32,309 --> 00:46:31,200
capacitor continues to recharge

1233
00:46:33,750 --> 00:46:32,319
in my book that's a second law of

1234
00:46:35,589 --> 00:46:33,760
violation so

1235
00:46:37,349 --> 00:46:35,599
um i realize that you've circumscribed

1236
00:46:39,349 --> 00:46:37,359
your system carefully but could you

1237
00:46:40,829 --> 00:46:39,359
expand it please to a situation where

1238
00:46:43,109 --> 00:46:40,839
you're doing external

1239
00:46:45,670 --> 00:46:43,119
work let's say on something like what

1240
00:46:48,069 --> 00:46:45,680
garrett said a motor or

1241
00:46:50,470 --> 00:46:48,079
tv or whatever it happens to be if it's

1242
00:46:54,390 --> 00:46:50,480
doing external work does it still not

1243
00:46:56,950 --> 00:46:55,910
okay well this one took a year and a

1244
00:46:59,670 --> 00:46:56,960
half

1245
00:47:02,150 --> 00:46:59,680
and i always hate to speculate on like

1246
00:47:04,069 --> 00:47:02,160
maybe the next circuit we should study

1247
00:47:06,550 --> 00:47:04,079
or the next situation

1248
00:47:09,349 --> 00:47:06,560
uh but um

1249
00:47:14,950 --> 00:47:12,230
draw say something kind of related and i

1250
00:47:17,750 --> 00:47:14,960
think it i think it'll support my point

1251
00:47:18,870 --> 00:47:17,760
and give some clarity to your question

1252
00:47:21,430 --> 00:47:18,880
um

1253
00:47:23,190 --> 00:47:21,440
if in in you know we like to talk about

1254
00:47:25,270 --> 00:47:23,200
feynman's brownie and ratchet you know

1255
00:47:27,510 --> 00:47:25,280
he says if you stick a windmill in your

1256
00:47:29,270 --> 00:47:27,520
room and the air is not flowing at all

1257
00:47:32,150 --> 00:47:29,280
then it's not going to sit and turn the

1258
00:47:34,309 --> 00:47:32,160
windmill you know basically

1259
00:47:36,630 --> 00:47:34,319
so that's kind of a thermodynamic

1260
00:47:38,630 --> 00:47:36,640
equilibrium position that you're sitting

1261
00:47:42,069 --> 00:47:38,640
in but but

1262
00:47:44,710 --> 00:47:42,079
i i bet you don't disagree with this if

1263
00:47:46,470 --> 00:47:44,720
i take this mass off this balloon will

1264
00:47:48,309 --> 00:47:46,480
expand and raise it

1265
00:47:51,829 --> 00:47:48,319
so what we're really doing is we're

1266
00:47:54,549 --> 00:47:51,839
creating a system that has uh an

1267
00:47:55,670 --> 00:47:54,559
unbalanced set of forces that drives the

1268
00:47:57,670 --> 00:47:55,680
system

1269
00:47:59,589 --> 00:47:57,680
in one direction to balance out the

1270
00:48:02,150 --> 00:47:59,599
forces just maybe like water going off a

1271
00:48:04,870 --> 00:48:02,160
waterfall so there's unbalanced forces

1272
00:48:06,630 --> 00:48:04,880
in the system and they drive the system

1273
00:48:09,349 --> 00:48:06,640
in one direction nothing wrong with the

1274
00:48:11,349 --> 00:48:09,359
laws of physics or thermodynamics there

1275
00:48:14,549 --> 00:48:11,359
and that's exactly where this work comes

1276
00:48:16,470 --> 00:48:14,559
from is from those forces doing work and

1277
00:48:18,870 --> 00:48:16,480
entropy you know you kind of went

1278
00:48:20,790 --> 00:48:18,880
through this nice little argument here

1279
00:48:23,030 --> 00:48:20,800
you know you can you can connect all the

1280
00:48:26,069 --> 00:48:23,040
dots together in a night in an ideal

1281
00:48:27,589 --> 00:48:26,079
picture um i i honestly thought well

1282
00:48:28,470 --> 00:48:27,599
yeah i should let you answer but i kind

1283
00:48:29,750 --> 00:48:28,480
of was

1284
00:48:31,829 --> 00:48:29,760
thought you might be interested the

1285
00:48:33,990 --> 00:48:31,839
entropy does decay it's a it's a

1286
00:48:36,549 --> 00:48:34,000
well-controlled thing here does decrease

1287
00:48:38,470 --> 00:48:36,559
in time as the capacitors charge there's

1288
00:48:40,069 --> 00:48:38,480
some organization that's happening as

1289
00:48:41,910 --> 00:48:40,079
the capacitor starts a very interesting

1290
00:48:43,349 --> 00:48:41,920
thing but anyhow just try to throw that

1291
00:48:45,670 --> 00:48:43,359
out there yeah so i i kind of would

1292
00:48:47,910 --> 00:48:45,680
point you to this it's a non-equilibrium

1293
00:48:49,910 --> 00:48:47,920
there's unbalanced forces there's no

1294
00:48:52,470 --> 00:48:49,920
problem here with this with this thing

1295
00:48:54,309 --> 00:48:52,480
doing work the difference here is that

1296
00:48:56,150 --> 00:48:54,319
with the gas there's internal energy

1297
00:48:57,829 --> 00:48:56,160
that's then being converted into work

1298
00:48:59,430 --> 00:48:57,839
right and if you add the mass back and

1299
00:49:01,349 --> 00:48:59,440
you kind of revert to your initial

1300
00:49:02,790 --> 00:49:01,359
position there'll be no energy gain

1301
00:49:04,230 --> 00:49:02,800
because all that energy goes back in the

1302
00:49:05,990 --> 00:49:04,240
potential the gas

1303
00:49:07,750 --> 00:49:06,000
versus in our in your system it sounds

1304
00:49:09,670 --> 00:49:07,760
like you're able to

1305
00:49:11,750 --> 00:49:09,680
complete a cycle and have this energy

1306
00:49:14,710 --> 00:49:11,760
extracted so yeah

1307
00:49:15,670 --> 00:49:14,720
okay yeah no no thanks paul so so okay

1308
00:49:16,950 --> 00:49:15,680
so

1309
00:49:18,710 --> 00:49:16,960
let's

1310
00:49:23,910 --> 00:49:18,720
it's a little different than i think you

1311
00:49:23,920 --> 00:49:27,990
you muted yourself

1312
00:49:33,109 --> 00:49:30,790
i think you're muted

1313
00:49:35,430 --> 00:49:33,119
paul we can't hear you oh okay so sorry

1314
00:49:37,270 --> 00:49:35,440
i'm back now somehow muted muted me

1315
00:49:40,309 --> 00:49:37,280
sorry about that so okay

1316
00:49:42,870 --> 00:49:40,319
so um let's go back to this picture here

1317
00:49:45,829 --> 00:49:42,880
so if i take the second mass which i

1318
00:49:49,030 --> 00:49:45,839
slid off let's say i have to raise it to

1319
00:49:51,589 --> 00:49:49,040
h and set it back down on here and then

1320
00:49:54,150 --> 00:49:51,599
it will compress this back down

1321
00:49:56,630 --> 00:49:54,160
so i have to do some work on the mass

1322
00:49:59,030 --> 00:49:56,640
and then it'll compress the gas back and

1323
00:50:01,270 --> 00:49:59,040
i can now do work on the environment put

1324
00:50:02,470 --> 00:50:01,280
energy back into the environment from

1325
00:50:03,990 --> 00:50:02,480
myself

1326
00:50:06,230 --> 00:50:04,000
so how do i do that with mine well i

1327
00:50:09,270 --> 00:50:06,240
take the capacitors away from the

1328
00:50:11,190 --> 00:50:09,280
circuit i hook them up to resistors they

1329
00:50:13,190 --> 00:50:11,200
discharge through the resistor

1330
00:50:14,470 --> 00:50:13,200
dissipating energy back to the

1331
00:50:16,790 --> 00:50:14,480
environment

1332
00:50:20,710 --> 00:50:19,430
it's the same thing but i will give you

1333
00:50:25,190 --> 00:50:20,720
something

1334
00:50:28,230 --> 00:50:25,200
i can put my finger on it

1335
00:50:30,309 --> 00:50:28,240
i can take that empty capacitor hook it

1336
00:50:32,710 --> 00:50:30,319
back up to the circuit it will recharge

1337
00:50:35,030 --> 00:50:32,720
itself it's like i'm getting it for free

1338
00:50:37,430 --> 00:50:35,040
here i had to raise the mass to get it

1339
00:50:40,790 --> 00:50:37,440
back to the initial condition right yeah

1340
00:50:44,630 --> 00:50:40,800
so there's some element of freeness here

1341
00:50:49,670 --> 00:50:44,640
that's happening but it's really because

1342
00:50:52,470 --> 00:50:49,680
the the diodes have this voltage in them

1343
00:50:54,150 --> 00:50:52,480
and they're trying to their equilibrium

1344
00:50:55,829 --> 00:50:54,160
is different than the earth's

1345
00:50:58,390 --> 00:50:55,839
equilibrium

1346
00:51:00,069 --> 00:50:58,400
sure anyhow it's it's a it's a very

1347
00:51:03,190 --> 00:51:00,079
interesting system and i hope other

1348
00:51:06,150 --> 00:51:03,200
people will look at it too

1349
00:51:08,950 --> 00:51:06,160
there's so many questions i just to push

1350
00:51:10,710 --> 00:51:08,960
into what what paul was just saying so

1351
00:51:13,030 --> 00:51:10,720
both daniel and i are talking about

1352
00:51:16,390 --> 00:51:13,040
bleeding the energy off continuously as

1353
00:51:17,670 --> 00:51:16,400
opposed to switching back and forth

1354
00:51:18,549 --> 00:51:17,680
uh

1355
00:51:23,030 --> 00:51:18,559
can you

1356
00:51:27,410 --> 00:51:25,829
yes so um

1357
00:51:28,790 --> 00:51:27,420
so you're basically saying

1358
00:51:34,390 --> 00:51:28,800
[Music]

1359
00:51:38,870 --> 00:51:36,470
somehow hook up a circuit here with the

1360
00:51:41,829 --> 00:51:38,880
resistor

1361
00:51:44,150 --> 00:51:41,839
right here so it draws current

1362
00:51:48,150 --> 00:51:44,160
off this thing

1363
00:51:50,390 --> 00:51:48,160
but the rate of current is basically

1364
00:51:52,390 --> 00:51:50,400
such that it doesn't just pull it all

1365
00:51:53,270 --> 00:51:52,400
off you know it kind of does it at some

1366
00:51:55,990 --> 00:51:53,280
certain

1367
00:51:57,829 --> 00:51:56,000
right rate

1368
00:51:59,829 --> 00:51:57,839
so basically that's going to be taking

1369
00:52:01,750 --> 00:51:59,839
the energy of the capacitor again

1370
00:52:03,109 --> 00:52:01,760
putting it back into the thermal

1371
00:52:05,430 --> 00:52:03,119
environment

1372
00:52:07,750 --> 00:52:05,440
that that originally came from

1373
00:52:09,510 --> 00:52:07,760
you know you know to some extent

1374
00:52:11,910 --> 00:52:09,520
you know people don't didn't i don't

1375
00:52:13,510 --> 00:52:11,920
think really got this but

1376
00:52:16,150 --> 00:52:13,520
um

1377
00:52:18,470 --> 00:52:16,160
i like to think honestly this paper was

1378
00:52:21,270 --> 00:52:18,480
almost more significant here we're

1379
00:52:24,309 --> 00:52:21,280
powering the circuit directly

1380
00:52:26,309 --> 00:52:24,319
from the thermal environment

1381
00:52:28,549 --> 00:52:26,319
and it's doing work it can do work it

1382
00:52:30,790 --> 00:52:28,559
can power a circuit

1383
00:52:33,030 --> 00:52:30,800
that's really

1384
00:52:34,870 --> 00:52:33,040
to me was more significant but honestly

1385
00:52:37,430 --> 00:52:34,880
i got so much

1386
00:52:39,510 --> 00:52:37,440
mail about well you're not really doing

1387
00:52:41,829 --> 00:52:39,520
anything useful what if you charged a

1388
00:52:44,069 --> 00:52:41,839
capacitor and you stole energy from the

1389
00:52:46,630 --> 00:52:44,079
earth then you'd be doing something now

1390
00:52:49,109 --> 00:52:46,640
you're doing something real so actually

1391
00:52:50,630 --> 00:52:49,119
we did do that we did steal energy from

1392
00:52:51,990 --> 00:52:50,640
the environment we maybe we did

1393
00:52:53,670 --> 00:52:52,000
something real

1394
00:52:55,910 --> 00:52:53,680
but now you're gonna now you're kind of

1395
00:52:57,510 --> 00:52:55,920
wanting to go back to the earlier one

1396
00:53:00,230 --> 00:52:57,520
you realize in your question well what

1397
00:53:02,950 --> 00:53:00,240
if i just use it directly right that's

1398
00:53:04,790 --> 00:53:02,960
just an easier problem okay fascinating

1399
00:53:07,190 --> 00:53:04,800
thank you yeah

1400
00:53:08,549 --> 00:53:07,200
quick questions uh james lee and then

1401
00:53:10,630 --> 00:53:08,559
tom vallone

1402
00:53:16,309 --> 00:53:10,640
yeah

1403
00:53:19,030 --> 00:53:16,319
solid i'm so pretty to see

1404
00:53:21,589 --> 00:53:19,040
as daniel and also um

1405
00:53:23,910 --> 00:53:21,599
talk about it it's actually your process

1406
00:53:25,910 --> 00:53:23,920
actually built a very nice

1407
00:53:27,750 --> 00:53:25,920
type of b energy process we now

1408
00:53:29,910 --> 00:53:27,760
discovered in

1409
00:53:31,910 --> 00:53:29,920
my work actually in biology exists in

1410
00:53:32,950 --> 00:53:31,920
your body in my body in the whole world

1411
00:53:34,390 --> 00:53:32,960
actually

1412
00:53:36,950 --> 00:53:34,400
so um

1413
00:53:38,790 --> 00:53:36,960
yes your intuitive component as you said

1414
00:53:40,710 --> 00:53:38,800
uh you know follow the second law very

1415
00:53:43,510 --> 00:53:40,720
very well okay like your capacity

1416
00:53:46,630 --> 00:53:43,520
charging you know all that but your

1417
00:53:50,150 --> 00:53:46,640
overall process as any point yeah

1418
00:53:52,069 --> 00:53:50,160
you are now exchanging heat energy from

1419
00:53:54,549 --> 00:53:52,079
you know charging can become useful

1420
00:53:56,710 --> 00:53:54,559
energy right so you can do work

1421
00:53:59,829 --> 00:53:56,720
actually so you don't be afraid of um

1422
00:54:01,750 --> 00:53:59,839
you don't this in that case your energy

1423
00:54:04,230 --> 00:54:01,760
b process actually the second one does

1424
00:54:06,069 --> 00:54:04,240
not apply we'll talk more about it

1425
00:54:08,069 --> 00:54:06,079
so don't be afraid you know saying hey

1426
00:54:09,990 --> 00:54:08,079
you know this second knot does not pie

1427
00:54:11,589 --> 00:54:10,000
because you do see a phenomenon you say

1428
00:54:12,870 --> 00:54:11,599
getting something you know interesting

1429
00:54:14,390 --> 00:54:12,880
as you said

1430
00:54:16,069 --> 00:54:14,400
unusual right

1431
00:54:17,829 --> 00:54:16,079
yeah so that's my point

1432
00:54:20,069 --> 00:54:17,839
yeah i agree i think the second law

1433
00:54:22,630 --> 00:54:20,079
doesn't apply because they're unbalanced

1434
00:54:24,870 --> 00:54:22,640
forces we're driving the system

1435
00:54:27,349 --> 00:54:24,880
and like letting water go off a cliff of

1436
00:54:29,349 --> 00:54:27,359
course you can harvest energy from that

1437
00:54:31,030 --> 00:54:29,359
and it's just um it's just out of

1438
00:54:33,030 --> 00:54:31,040
equilibrium

1439
00:54:35,190 --> 00:54:33,040
yeah so daniel and i also talk about you

1440
00:54:37,270 --> 00:54:35,200
have a symmetrical process there when

1441
00:54:39,510 --> 00:54:37,280
it's symmetric going on

1442
00:54:41,990 --> 00:54:39,520
as at any point you are so the second

1443
00:54:44,470 --> 00:54:42,000
one be careful sometimes you can apply

1444
00:54:46,630 --> 00:54:44,480
sometimes you don't apply

1445
00:54:50,230 --> 00:54:46,640
so that's my point thank you wonderful

1446
00:54:50,240 --> 00:54:53,510
tom

1447
00:54:53,520 --> 00:54:59,910
uh you're muted

1448
00:55:03,670 --> 00:55:01,829
my tom i can't hear you

1449
00:55:06,309 --> 00:55:03,680
okay um

1450
00:55:08,870 --> 00:55:06,319
yeah how you doing i i'm the author of

1451
00:55:12,630 --> 00:55:08,880
the book on practical conversion zero

1452
00:55:15,430 --> 00:55:12,640
point energy um i haven't corresponded

1453
00:55:17,670 --> 00:55:15,440
with you yet but i've been a great fan

1454
00:55:19,430 --> 00:55:17,680
and i wanted to call your attention to

1455
00:55:21,670 --> 00:55:19,440
johnson noise

1456
00:55:26,950 --> 00:55:21,680
1927 fizzrev

1457
00:55:28,710 --> 00:55:26,960
um also kellen and welton uh in 1951 and

1458
00:55:31,030 --> 00:55:28,720
also estumian

1459
00:55:33,030 --> 00:55:31,040
those are references that might actually

1460
00:55:34,470 --> 00:55:33,040
start you in the direction of including

1461
00:55:36,870 --> 00:55:34,480
zero point energy

1462
00:55:40,390 --> 00:55:36,880
uh one half h nu

1463
00:55:43,750 --> 00:55:40,400
and it could be another factor that's

1464
00:55:46,230 --> 00:55:43,760
adding to the input energy especially if

1465
00:55:47,109 --> 00:55:46,240
the temperature changes and starts to go

1466
00:55:48,789 --> 00:55:47,119
down

1467
00:55:50,230 --> 00:55:48,799
that's the test for

1468
00:55:51,990 --> 00:55:50,240
whether zero point energy is a

1469
00:55:54,789 --> 00:55:52,000
contribution

1470
00:55:57,750 --> 00:55:54,799
coke or coach koch

1471
00:55:59,030 --> 00:55:57,760
did experiments at liquid nitrogen

1472
00:56:01,270 --> 00:55:59,040
temperatures did with helium

1473
00:56:03,750 --> 00:56:01,280
temperatures actually and still found

1474
00:56:05,510 --> 00:56:03,760
oscillations and and fluctuations that

1475
00:56:07,430 --> 00:56:05,520
are available so they're non-thermal

1476
00:56:09,109 --> 00:56:07,440
fluctuations that could be contributing

1477
00:56:10,710 --> 00:56:09,119
to the effect you're having

1478
00:56:13,829 --> 00:56:10,720
yeah thanks for that you know i'm a big

1479
00:56:17,270 --> 00:56:13,839
fan of johnson noise and nyquist uh

1480
00:56:19,510 --> 00:56:17,280
theory that i pointed out the imaginary

1481
00:56:21,670 --> 00:56:19,520
part and the real part here actually as

1482
00:56:23,750 --> 00:56:21,680
kind of a nod to them because that's

1483
00:56:25,829 --> 00:56:23,760
really what he originally proved was the

1484
00:56:28,309 --> 00:56:25,839
real part is the important part kind of

1485
00:56:30,309 --> 00:56:28,319
the power but you can control the gain

1486
00:56:31,829 --> 00:56:30,319
with the imaginary part so i kind of

1487
00:56:33,030 --> 00:56:31,839
that's an interesting

1488
00:56:36,950 --> 00:56:33,040
factor here

1489
00:56:40,230 --> 00:56:36,960
but yeah i never thought about the um

1490
00:56:41,990 --> 00:56:40,240
the zero point energy um here before so

1491
00:56:43,750 --> 00:56:42,000
that i'll i'll take a look at that too

1492
00:56:46,069 --> 00:56:43,760
that's a good question i'll send you the

1493
00:56:47,910 --> 00:56:46,079
books i've got and references and

1494
00:56:49,109 --> 00:56:47,920
hopefully help you along

1495
00:56:54,549 --> 00:56:49,119
thank you

1496
00:56:58,150 --> 00:56:54,559
call it there so that we can take a

1497
00:57:00,390 --> 00:56:58,160
one-minute break before the next talk

1498
00:57:02,390 --> 00:57:00,400
so thank you again for a fascinating

1499
00:57:03,670 --> 00:57:02,400
talk and i look forward to talking more

1500
00:57:05,670 --> 00:57:03,680
about this

1501
00:57:07,109 --> 00:57:05,680
uh in the panel discussion with you this